IGCSE Math B 8.K Combined transformations Topic Practice

The diagram shows kite A.
Kite B is the image of kite A under a reflection in the line with equation y=-1.

Kite A is transformed to kite C by a reflection in the line with equation x=4 followed by the translation
$$\begin{pmatrix}-8\\-6\end{pmatrix}.$$
Kite C is the image of kite B under a rotation through $180^\circ$ about the point P.

On the grid opposite, draw and label kite C.

The vertices of triangle A are the points with coordinates (2,2),(3,2) and (2,4).

Describe fully the single transformation that maps triangle C onto triangle A.

Triangle A and triangle B are drawn on the grid opposite.
Triangle A is transformed to triangle C under the translation $\begin{pmatrix}-4\\7\end{pmatrix}$.

Triangle B is the image of triangle A under an enlargement with centre the origin and scale factor $\sqrt5$, followed by a clockwise rotation of $\theta^\circ$ about the origin.
Calculate the value, to 4 significant figures, of $\theta$.
Show your working.

Two triangles, A and B, are shown on the grid on the next page.

Describe fully the single transformation that maps triangle A onto triangle E.

Only use this grid if you need to redraw your triangles.

The triangle A has vertices with coordinates (-5,2), (-11,0) and (-7,6).

Describe fully the single transformation that maps triangle C onto triangle A.

Only use this grid if you need to redraw your triangles.